Basic properties
| Modulus: | \(8032\) | |
| Conductor: | \(8032\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(1000\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8032.cl
\(\chi_{8032}(29,\cdot)\) \(\chi_{8032}(37,\cdot)\) \(\chi_{8032}(53,\cdot)\) \(\chi_{8032}(61,\cdot)\) \(\chi_{8032}(77,\cdot)\) \(\chi_{8032}(109,\cdot)\) \(\chi_{8032}(133,\cdot)\) \(\chi_{8032}(141,\cdot)\) \(\chi_{8032}(165,\cdot)\) \(\chi_{8032}(213,\cdot)\) \(\chi_{8032}(229,\cdot)\) \(\chi_{8032}(269,\cdot)\) \(\chi_{8032}(277,\cdot)\) \(\chi_{8032}(285,\cdot)\) \(\chi_{8032}(293,\cdot)\) \(\chi_{8032}(333,\cdot)\) \(\chi_{8032}(341,\cdot)\) \(\chi_{8032}(349,\cdot)\) \(\chi_{8032}(381,\cdot)\) \(\chi_{8032}(397,\cdot)\) \(\chi_{8032}(413,\cdot)\) \(\chi_{8032}(421,\cdot)\) \(\chi_{8032}(429,\cdot)\) \(\chi_{8032}(437,\cdot)\) \(\chi_{8032}(453,\cdot)\) \(\chi_{8032}(461,\cdot)\) \(\chi_{8032}(485,\cdot)\) \(\chi_{8032}(493,\cdot)\) \(\chi_{8032}(557,\cdot)\) \(\chi_{8032}(573,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{1000})$ |
| Fixed field: | Number field defined by a degree 1000 polynomial (not computed) |
Values on generators
\((6527,3013,257)\) → \((1,e\left(\frac{3}{8}\right),e\left(\frac{83}{250}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 8032 }(29, a) \) | \(-1\) | \(1\) | \(e\left(\frac{437}{1000}\right)\) | \(e\left(\frac{107}{200}\right)\) | \(e\left(\frac{43}{500}\right)\) | \(e\left(\frac{437}{500}\right)\) | \(e\left(\frac{927}{1000}\right)\) | \(e\left(\frac{49}{1000}\right)\) | \(e\left(\frac{243}{250}\right)\) | \(e\left(\frac{17}{250}\right)\) | \(e\left(\frac{741}{1000}\right)\) | \(e\left(\frac{523}{1000}\right)\) |